Abstract: In this paper, a single period inventory model with resalable returns has been analyzed in an imprecise and uncertain mixed environment. Demand has been introduced as a fuzzy random variable. In this model, a single order is placed before the start of the selling season. The customer, for a full refund, may return purchased products within a certain time interval. Returned products are resalable, provided they arrive back before the end of the selling season and are found to be undamaged. Products remaining at the end of the season are salvaged. All demands not met directly are lost. The probabilities that a sold product is returned and that a returned product is resalable, both imprecise in a real situation, have been assumed to be fuzzy in nature.
Abstract: Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.
Abstract: Inventory decisional environment of short life-cycle
products is full of uncertainties arising from randomness and
fuzziness of input parameters like customer demand requiring
modeling under hybrid uncertainty. Prior inventory models
incorporating fuzzy demand have unfortunately ignored stochastic
variation of demand. This paper determines an unambiguous optimal
order quantity from a set of n fuzzy observations in a newsvendor
inventory setting in presence of fuzzy random variable demand
capturing both fuzzy perception and randomness of customer
demand. The stress of this paper is in providing solution procedure
that attains optimality in two steps with demand information
availability in linguistic phrases leading to fuzziness along with
stochastic variation. The first step of solution procedure identifies
and prefers one best fuzzy opinion out of all expert opinions and the
second step determines optimal order quantity from the selected
event that maximizes profit. The model and solution procedure is
illustrated with a numerical example.